1. Field of the Invention
The present invention relates to a device and a method for modeling a cornea. In particular, the present invention relates to a computerized device and a computer-implemented method for modeling a cornea for simulating tissue cuts in the cornea, wherein the computerized device comprises a processor programmed to generate a patient-specific finite element model of the cornea.
2. Description of the Prior Art
A plurality of refractive errors such as myopia (shortsightedness), hyperopia (farsightedness) or astigmatism are corrected these days by means of surgical interventions on the eye. Here, the refractive correction of the eye is predominantly brought about by means of ophthalmological laser systems, which cut and/or ablate the eye tissue, in particular the cornea, in order to approximate the optical refractive power of the eye as closely as possible to a desired value. Although tissue cuts can be carried out very precisely by means of laser pulses—much more accurately compared to e.g. manually using a scalpel—the change in the tissue form emerging in the case of tissue cuts as a result of the intraocular pressure makes the planning of cuts and the prediction of cut results nevertheless very difficult.
In order to improve the ophthalmic refractive correction, WO 02/07660, WO 94/18636, US 2009/318907 and US 2009/187386 describe the modeling of the eye using finite element analysis. Here, the finite element model of the eye can be used for simulating tissue cuts. WO 02/07660 describes the introduction of a layer model of the cornea with a plurality of layers with different strengths. US 2009/318907 and US 2009/187386 describe a general axis-symmetrical model based on a nonlinear elastic, slightly compressible and transversely isotropic formulation. US 2009/187386 moreover describes a connection of the cornea to the sclera with pre-programming of peripheral elements for imaging a secure connection of the cornea to the sclera (limbus), which may not be sufficient in the case of cuts which extend beyond the cornea into the adjacent sclera. Moreover, the known solutions provide no indications as to how the stromal swelling pressure is included in the modeling.
In recent years, the inhomogeneity of the cornea over the depth thereof was examined in great detail, particularly in:    Quantock A J, Boote C, Yount R D, Hayes S, Tanioka H, Kawasaki S, Ohta N, Iida T, Yagi N, Kinoshita S, Meek K M, (2007); “Small-angle fibre diffraction studies of corneal matrix structure: a depth-profiled investigation of the human eye-bank cornea”; Journal of Applied Crystallography, 40: 335-340;    Palka B P, Tanioka H, Sotozono C, Yagi N, Boote C, Young R D, Meek K M, Quantock A J, (2008); “Reduced collagen interfibrillar spacing in macular corneal dystrophy occurs predominantly in deep stromal layers”; Investigative Ophthalmology & Visual Science, 49: E-Abstract 3926;    Kamma-Lorger C S, Boote C, Young R D, Hayes S, Quantock A J, Meek K M, (2008); “Depth profile study of molecular collagen structure in normal human cornea; Acta Ophthalmologica”, 86: 243;    Meek K M, Boote C, (2009); “The use of X-ray scattering techniques to quantify the orientation and distribution of collagen in the corneal stroma”; Progress in Retinal and Eye Research, 28: 369-392;    Kamma-Lorger C S, Boote C, Hayes S, Moger J, Burghammer M, Knupp C, Quantock A J, Sorensen T, Di Cola E, White N, Young R D, Meek K M, (2010); “Collagen and mature elastic fibre organization as a function of depth in the human cornea and limbus”; Journal of Structural Biology, 169: 424-430; and    Petsche S J, Chernayak D, Martiz J, Levenston M E, Pinsky P M, (2012); “Depth-Dependent Transverse Shear Properties of the Human Corneal Stroma”; Investigative Ophthalmology & Visual Science, 53(2): 873-80.
What was identified here is that the tissue becomes ever weaker over the depth thereof, i.e. from the front/outside (anterior) to the back/inside (posterior), and, in particular, that there is a significant reduction in the shearing stiffness. The cause of this was found to lie in the fact that there are many inclined collagen fibers, i.e. collagen fibers that do not extend parallel to the corneal surface, in the front/outer layers. Inclined fibers, or so-called cross-linked fibers, provide the tissue with shearing stiffness. By contrast, the fibers lying properly on one another in layers, extending parallel to the surface, are found in the deep (back/inside) layers.
In the last decade, various mathematical material definitions were established and published for simulating the biomechanical properties of the corneal tissue, particularly in:    Bryant M, McDonnell P, (1996); “Constitutive laws for biomechanical modelling of refractive surgery”, Journal of Biomechanical Engineering, 118(4): 473-481;    Pinsky P M, Van der Heide D, Chernyak D, (2005); “Computational modelling of mechanical anisotropy in the cornea and sclera”; Journal of Cataract and Refractive Surgery, 31(1): 136-145;    Alastrue V, Calvo B, Pena E, Doblare M, (2006); “Biomechanical Modelling of Refractive Surgery; Journal of Biomechanical Engineering”, 128: 150;    Lanchares E, Calvo B, Cristobal J, Doblare M, (2008); “Finite element simulation of arcuates for astigmatism correction”; Journal of Biomechanics, 41: 797-805;    Pandolfi A, Manganiello F, (2006); “A model for the human cornea: constitutive formulation and numerical analysis”; Biomechanics and Modelling in Mechanobiology, 5(4): 237-246;    Pandolfi A, Holzapfel G, (2008); “Three-dimensional modelling and computational analysis of the human cornea considering distributed collagen fibril orientations”; Journal of Biomechanical Engineering, 130(6); and    Pandolfi A, Fotia G, Manganiello F, (2009); “Finite element simulation of laser refractive corneal surgery”; Engineering with Computers, 25: 15-24.
Generating a patient-specific finite element model of the cornea was described in the document Studer H P, Riedwyl H, Amstutz C A, Hanson V M, Büchler P, (2013) “Patient-specific finite-element simulation of the human cornea: A clinical validation study on cataract surgery”; Journal of Biomechanics, 46(4): 751-758. Here, the effect of cataract incisions on patients was simulated numerically. However, Studer et al. specifically state in this document that neither the material parameters nor the distribution of collagen fibers was patient-specific and that the depth-dependence of mechanical properties within the corneal thickness was also ignored. Moreover, as a conclusion, they noted that taking into account the individual corneal topography of the patient is more relevant to a precise prediction of the post-operative corneal form than a precise determination of patient-specific material properties.
Mathematical material definitions for simulating the biomechanical properties of the corneal tissue, in which the inclined fibers are also taken into account, are only found in the following documents:
Studer H P, Larrea X, Riedwyl H, Büchler P, (2010); “Biomechanical model of human cornea based on stromal microstructure”; Journal of Biomechanics, 43: 836-842; and
Petsche S J, Pinsky P M, (2013); “The role of 3-D collagen organization in stromal elasticity: a model based on X-ray diffraction data and second harmonic-generated images”; Biomechanics and Modelling in Mechanobiology.
Here, in the latter document, Petsche S J and Pinsky P M define a three-dimensional distribution function (all directions are in a spherical coordinate system), which simultaneously models the weighting of the main fibers and inclined fibers. By means of this weighting, the authors describe the amount of collagen fibers that extend in a specific direction. The fibers themselves are described as a material anisotropy in the continuum.